The Sun has not deceased. (At least I think not, though I can’t be certain; I meant to get this written during the day, but night has fallen.) The Sun has just been very late at every one of the places in our sky that it’s supposed to visit.

Back on November 3 the equation of time was at its yearly maximum of 16.5 minutes. Here is my graph again.

Now on Feb. 11 the equation of time has fallen to its minimum for the year, -14.25 minutes. It goes through the same cycle each year.

What this means is that at noon by the clock on November 3 the Sun had already passed through its highest point (on the meridian or north-south line) by 16.5 minutes. (By the “clock” we mean what the clock would be for the real place where you live, unadjusted for the middle of your time-zone.) Every day after that the Sun was a little later passing the meridian; on Dec. 25 it was exactly on time by the clock; it kept arriving a bit later; and now when the clock shows 12 noon the Sun is 14.25 minutes short of reaching the meridian. (It’s the same, or almost exactly so, for other times in the day, such as 9 AM or 3:15 PM or midnight when the Sun should be deepest below the horizon.)

Instead of re-explaining why this happens (as on Nov.3, or on page 33 of *Astronomical Calendar 2015*), how about we dip into the larger subject of my head’s lack of grip on numbers? If I sometimes seem to get anything to do with numbers right, it’s because of trying very hard. One of the devils in the world of numbers is the Two-Way Hazard. Does “Daylight-Saving Time” mean we’re calling the real 9 o’clock 8 or 10? Does it mean it’s like you’re in one time zone to the west or to the east? Is negative elongation east or west? Does azimuth start from the north and go westward or eastward, and which does position angle do? (It does the opposite, and I’m not going to stop and say what azimuth and position angle are.) Do I correct Ephemeris Time to Universal Time by adding or subtracting Delta-T? That last is a dangerous thing to get wrong; the equation of time is a fairly harmless trap set by this devil – getting it the wrong way around would only, I think, affect discussions, like this, of the equation of time.

The equation of time is the number that “equates” the real time when the Sun crosses the meridian (or other point in the sky) to the average time when it should. Let (as the algebraists say) E be the equation of time. Let M be the mean time, which our steady clock shows. Let A be the apparent time, by the actual Sun. (*Apparent* is another example of the slitheriness of natural language: sometimes it means that a thing appears so but is not so; in this case it means that we’re talking about where the Sun really appears.)

So what do we do with E? Add or subtract it, to or from what? I never just remember this, I have to re-picture it.

We subtract it from A to make M, and so the equation (in the other and better known sense) can be written in three ways:

E = A – M

M = A – E

A = M + E

So if what we want to find is today’s A (apparent, or real, time) when M is 12 noon, then it is M plus E; so, today’s E being a negative number, A is 12h 00m + (-14.25m), which is 11h 45.75m, otherwise known as 11:45.75. *That’s* what the real Sun time is when the clock says it’s 12.

As you may feel along with me, the Two-Way Hazard is only one of the devils in the world of numbers.

Gazooks! It’s all still so confusing to me, but I think I’m beginning to get it. I’m still unsure now of how I should answer someone who asks me what time it is.

One think I love doing is asking someone whom I’ve just seen looking at his watch what time it is and see if he needs to look at it again in order to tell me the time. Did he not pay attention to the time it was when he first looked at his watch? Does anybody really know what time it is? Does anybody really care?, Lyrics from a 70’s tune by Chicago. Does anybody even remember that song? Just checking.

Discussing the Concept of Zero with you Son:

Shepard’s used to draw in the sand the count of sheep one would have at the end of a business transaction. Two lines in the sand meant you were left with two sheep, three meant you would get three sheep.

If the transaction had a result that would leave you with no sheep they would draw a circle representing the empty corral. ” O ” Zero.

Probably got this story from some astronomical calendar. ;-)

Very helpful.

At present I am discussing the concept of zero with my son. When he is doing his math homework he wants to know how zero can be both “nothing” and an “entity” in his equations. I’m terrible at this stuff, because I have never been able to really believe in nothingness, infinity, nor time. Oh and life without cheese.